Determination and measurement of solid–liquid equilibrium for binary fatty acid mixtures based on NRTL and UNIQUAC activity models

  • Seyed Mohammadreza Mirpoorian
  • MohammadHassan Vakili
  • Seyed Hossein Noie BaghbanEmail author
  • Pejman Roohi


The estimation of solid–liquid phase equilibrium is important for the design, development, and operation of many industrial processes because of application in many manufacturing fields such as cosmetic, pharmaceutic, and biotechnology industries. In this work, we measured solid–liquid phase equilibrium of six fatty acid binary mixtures using the DSC technique and developed thermodynamic approaches for binary fatty acid mixtures to estimate melting temperatures as a function of mole fraction in solid–liquid phase equilibrium. Derivation of NRTL and UNIQUAC activity models was developed to predict melting temperatures and latent heat to achieve eutectic points of undecylic acid, pentadecylic acid, margaric acid, and stearic acid six pairwise binary mixtures. The fatty acids eutectic mixtures are appropriate for heat water systems, phase clothes, concrete, and other similar applications. The results showed low deviations from experimental data measured in this study.


Fatty acid Wilson model Melting temperature Eutectic point 


  1. 1.
    Rocha SA, Guirardello R. An approach to calculate solid–liquid phase equilibrium for binary mixtures. Fluid Phase Equilib. 2009;281:12–21.CrossRefGoogle Scholar
  2. 2.
    Rangaiah GP. Evaluation of genetic algorithms and simulated annealing for phase equilibrium and stability problems. Fluid Phase Equilib. 2001;187–188:83–109.CrossRefGoogle Scholar
  3. 3.
    Rocha SA, daSilva LK, Boros LAD, Krahenbuhl MA, Guirardello R. Solid–liquid equilibrium calculation and parameters determination in thermodynamic models for binary and ternary fatty mixtures. Chem Eng Trans. 2014;37:535–40.Google Scholar
  4. 4.
    Tamura K, Kasuga T, Nakagawa T. Phase behavior and solid–liquid equilibria of aliphatic and aromatic carboxylic acid mixtures. Fluid Phase Equilib. 2016;420:24–9.CrossRefGoogle Scholar
  5. 5.
    Kopytowska AB, Górska A, Bryś J, Domian E, Wojdyła MW, Ligęza EO. Application of DSC and GC methods for characterization of newly designed spray-dried pea protein-fat preparations formulated with different types of a carbohydrate component. J Therm Anal Calorim. 2018;134:609–21.CrossRefGoogle Scholar
  6. 6.
    Marudova M, Momchilova M, Antova G, Petkova Z, Yordanov D, Zsivanovits G. Investigation of fatty acid thermal transitions and stability in poultry pates enriched with vegetable components. J Therm Anal Calorim. 2018;133:539–47.CrossRefGoogle Scholar
  7. 7.
    Razouk R, Beaumont O, Hay B. A new accurate calorimetric method for the enthalpy of fusion measurements up to 1000 °C. J Therm Anal Calorim. 2018. (in press).
  8. 8.
    Rolemberg MP. Solid-liquid balance of fatty acids and triglycerides: experimental determination of emodulation, Doctorate Thesis on Chemical Engineering, State University of Campinas, 2002.Google Scholar
  9. 9.
    Boros LAD. Mathematical modeling and thermodynamics of the solid-liquid balance of fatty systems, Master Thesis on Chemical Engineering, State University of Campinas, 2005.Google Scholar
  10. 10.
    Bruin S. Phase equilibria for food product and process design1. Fluid Phase Equilib. 1999;158–160:657–71.CrossRefGoogle Scholar
  11. 11.
    Huang CC, Chen YP. Measurements and model prediction of the solid–liquid equilibria of organic binary mixtures. Chem Eng Sci. 2000;55:3175–85.CrossRefGoogle Scholar
  12. 12.
    Slaughter DW, Doherty MF. Calculation of solid–liquid equilibrium and crystallization paths for melt crystallization processes. Chem Eng Sci. 1995;50:1679–94.CrossRefGoogle Scholar
  13. 13.
    Grondal BJ, Rogers DA. Melting points of binary fatty acid mixtures C6 to C12 and their application in the determination of purity. Oil Soap. 1944;21:303–5.CrossRefGoogle Scholar
  14. 14.
    Mu¨ller E, Stage H. Experimentelle Vermessung von Dampf-Flüssigkeits-Phasengleichgewichten. Berlin: Springer; 1961.CrossRefGoogle Scholar
  15. 15.
    Bailey AE. Melting and solidification of fats. New York: Interscience Publishers; 1950.Google Scholar
  16. 16.
    Wilson GM. Vapor–liquid equilibrium. XI. A new expression for the excess free energy of mixing. J Am Chem Soc. 1964;86:127–30.CrossRefGoogle Scholar
  17. 17.
    Renon H, Prausnitz JM. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968;14:135–44.CrossRefGoogle Scholar
  18. 18.
    Prausnitz JM, Lichtenthaler RN, Azevedo EG. Molecular thermodynamics of fluid-phase equilibria. New Jersey: Prectice-Hall; 1999.Google Scholar
  19. 19.
    Inoue T, Hisatsugu Y, Yamamoto R, Suzuki M. Solid–liquid phase behavior of binary fatty acid mixtures: 1. Oleic acid/stearic acid and oleic acid/behenic acid mixtures. Chem Phys Lipids. 2004;127:143–52.CrossRefPubMedGoogle Scholar
  20. 20.
    Haynes WM. CRC handbook of chemistry and physics. 95th ed. Boca Raton: CRC Press; 2014.Google Scholar
  21. 21.
    Wang TC, Lai TY, Chen YP. Solid–liquid equilibria for hexanedioic acid + benzoic acid, benzoic acid + pentanedioic acid, and hexanedioic acid + pentanedioic acid. J Chem Eng Data. 2010;55:5797–800.CrossRefGoogle Scholar
  22. 22.
    Cingolani A, Berchiesi G. Thermodynamic properties of organic compounds. J Therm Anal. 1974;6:87–90.CrossRefGoogle Scholar
  23. 23.
    Roux MV, Temprado M, Chickos JS, Nagano Y. Critically evaluated thermochemical properties of polycyclic aromatic hydrocarbons. J Phys Chem Ref Data. 2008;37:1855–996.CrossRefGoogle Scholar
  24. 24.
    Zhang Y, Su Y, Ge X. Prediction of the melting temperature and the fusion heat of (Quasi) eutectic PCM. J China Univ Sci Technol. 1995;25:474–8.Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Seyed Mohammadreza Mirpoorian
    • 1
  • MohammadHassan Vakili
    • 2
  • Seyed Hossein Noie Baghban
    • 1
    Email author
  • Pejman Roohi
    • 3
  1. 1.Department Chemical Engineering, Faculty of EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Department of Chemical Engineering, Shahreza BranchIslamic Azad UniversityShahrezaIran
  3. 3.National Iranian Gas CompanyIsfahanIran

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